# How many grams of NaOH are contained in 200 mL of a 0.400 M solution?

May 26, 2018

Approx. $3 \cdot g$

#### Explanation:

By definition....$\text{concentration"="moles of solute"/"volume of solution}$...and thus concentration has units of $m o l \cdot {L}^{-} 1$..

And following this definition dimensionally, $\text{moles of solute"="concentration"xx"volume}$..

And so here, this product gives...

$200 \cdot m L \times {10}^{-} 3 \cdot m L \cdot {L}^{-} 1 \times 0.400 \cdot m o l \cdot {L}^{-} 1 = {\underbrace{0.0800 \cdot m o l}}_{\text{moles of solute}}$..

And the associated mass is 0.0800*molxxunderbrace(40.00*g*mol^-1)_"molar mass of NaOH"=??*g

This is why chemists and physicists use units in their numerical calculations; not to confuse students, but to alert them when they have ballsed up a question. If the units didn't simplify to $m o l$ and $g$, we would know we had made an error...